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VC dimension for ternary classification problems

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lebesgue

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I am presently studying neural networks. I have a doubt regarding VC dimension concept. In case of the lecture which I heard, the dichotomy functions for "binary"pattern classification was done by a a class of dichotomies which perfectly shatters the m-dimensional space which contains the r training pattern vectors in which each vector is 2 dimensional in nature(2 dimensional inputs for the neuron). SUPPOSE for the same 2 input neuron, we are looking for a ternary pattern classification. Then what happens to the dichotomy functions? How we do pattern classification( the problematic area is how we shatter the space for a ternary pattern classification)? Will any new adjustable parameters be included? Please help me.. :oops:
 

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